全球三次样条格式数值模式动力框架与理想场试验研究

项目名称： 全球三次样条格式数值模式动力框架与理想场试验研究

项目编号： No.41275106

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 天文学、地球科学

项目作者： 辜旭赞

作者单位： 中国气象局武汉暴雨研究所

项目金额： 76万元

中文摘要： 本项目将具有对于原函数及其一阶、二阶导数"收敛性"和对于原函数二阶导数最佳逼近"最优性"等数学性质的三次样条函数引入到数值模式研究中，是对数值模式新方法、新选择的一种探索性创新基础研究。研究内容包括：全球精简（拓扑矩形）经纬网格设计与极区、极点处理；原始大气运动方程变量场三次样条格式二阶时空离散、求导与平滑方案；（二阶可导）三次样条插值求解上游点与三维散度场的准拉格朗日"时间分离+时间分片"积分方案；实现全球三次样条格式（格点）数值模式（无地形、静力）动力框架，对其进行平衡流试验、过极地气流试验、Rossby-Haurwitz波试验、长期积分强迫试验等一系列理想场试验，验证其科学性、精确性及程序正确性；并对其进行可扩展并行算法研究，提交全球三次样条格式数值模式动力框架串行算法和高效并行算法软件，为完成一个具有知识产权与发展前景的全球三次样条格式数值模式进行原创基础研究。

中文关键词： 三次样条函数；准拉格朗日时间分离积分方案；全球精简经纬网格；理想场试验；并行计算

英文摘要： In numerical analysis, cubic spline function consists of cubic spline, bi-cubic surface and tri-cubic (3-D cubic) cube, three based on the cubic spline interpolation (spline scheme), which posses the 2-order differentiable "convergence" and "optimality" of mathematical law, that are: 1) the cubic spline function, together with its first-order and second-order derivatives, contracts to the original function (contraction law); 2) its second-order derivative is optimal approximation to that of the original function (optimality law); 3) there exists periodic cubic spline. We are able to introduce the cubic spline functions into study of a numerical model, which will be a new method or new selection of basic research for innovation of meteorological numerical model (so called "spline model"). The research including: design of global reduced latitude-longitude rectangular mesh to treat both polar areas and Poles; spatial and temporal discretization, derivation and smooth with the spline scheme to variables in the meteorological primitive equations; quasi-Lagrangian time-split integration scheme of solving 3-D paths of all of the upstream points as well as their divergence field with fitting the cubic spline functions; bring about a new dynamic core of a global spline- scheme numerical model on the reduced latitude-lon

英文关键词： cubic spline function；quasi-Lagrangian time-split integration；global reduced latitude-longitude gird；exact test；parallel